One “air change” means moving a full room volume of air, so the identity is definitional: ACH = 60 × CFM ÷ volume in cubic feet, or in metric simply m³/h ÷ m³. It solves forward — a 200 CFM portable air cleaner in an 8,000 ft³ open plan delivers 60 × 200 ÷ 8,000 = 1.5 ACH — and backward: hitting 5 ACH in that same space needs 5 × 8,000 ÷ 60 = 667 CFM, more than one small unit can supply. The often more intuitive reading is minutes per complete change, 60 ÷ ACH: 1.5 ACH is a full change every 40 minutes.
Because volume sits in the denominator, the same airflow means wildly different ACH by room: 100 CFM turns over an 800 ft³ small office 7.5 times an hour but manages only 1.25 changes in a 4,800 ft³ family room, and ceiling height scales the answer linearly — the 7.5 ACH under an 8 ft ceiling drops to 5 at 12 ft.
A caution about targets: the “recommended ACH by room type” tables circulating online (bedrooms 5–6, kitchens 7–8) trace to no published standard. The citable residential requirement, ASHRAE 62.2, is airflow-based — a continuous whole-dwelling CFM rate plus local exhaust minimums of 100 CFM (intermittent) at kitchens and 50 CFM at baths — and true ACH mandates live mainly in healthcare, where ASHRAE 170 requires around 20 ACH in operating rooms and 12 in airborne-infection isolation rooms. Use the identity to convert between quantities; take the requirement from the standard governing the space.